A bar of mass $m$ resting on a smooth horizontal plane starts moving due to force $\left|\overrightarrow{F}\right|=\frac{mg}{9}$. The magnitude of the force remains constant with time. The force vector makes an angle $\theta$ with the horizontal which varies with the distance covered as $\mathrm{\theta }=\mathrm{Cx}$. If the constant $C=10 \left(\frac{ \mathrm{degree} }{\mathrm{meter} }\right),$ then the speed of the bar, when $\mathrm{\theta }$ becomes equal to $30°$ for the first time, is (Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.